Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.Scanner;
import java.util.Vector;

public class FunkyNumbers
{
	public static void main(String[] args)
	{
		Scanner input = new Scanner(System.in);
		int n = input.nextInt();
		Vector<Integer> nums = new Vector<Integer>();
		int temp;
		for (int k = 1; true; ++k)
		{
			temp = k * (k + 1) / 2;
			if (temp >= 1000000000)
			{
				break;
			}
			nums.add(temp);
		}
		int low = 0;
		int high = nums.size() - 1;
		while (low <= high)
		{
			temp = nums.get(low) + nums.get(high);
			if (temp == n)
			{
				System.out.println("YES");
				return;
			}
			else if (temp > n)
			{
				--high;
			}
			else
			{
				++low;
			}
		}
		System.out.println("NO");
	}
}